9. Let
$A = \begin{bmatrix} 3 & -1 & 0 & a \\ 2 & 0 & -1 & 0 \\ b & c & 0 & 4 \\ 0 & d & 0 & e \end{bmatrix}$
be a 4 by 4 matrix, where $a, b, c, d, e$ are some real numbers. Suppose that the trace of $A$ is 1, the
determinant of $A$ is -76, and $A$ has an eigenvector $(2, 1, 0, 1)$. Find the matrix $A$.
